LINKAGE, CROSSING-OVER, AND THE GERM PLASM 423 



tive positions of all known factors. The unit of distance on the map 

 is that between two genes that have a crossover value of i per 

 cent. Haldane has proposed the term morgan for this unit of map 

 distance. These map units are only relative units, not absolute, as 

 will be shown later. The validity of the crossing-over hypothesis and 

 of the chromosome maps may be tested in an almost infinite number of 

 ways. For example, let us take a simple case of the so-called three- 

 point method of locating a new factor. Suppose we have aheady 

 determined the crossover percentage for two factors A and 5 to be 6 

 per cent. A new factor, C, appears which belongs to the same linkage 

 group as -1 and B, and we wish to locate it. First we work out its 

 crossover percentage with A, and it turns out to be 4 per cent. We 

 then can predict that the crossover percentage between B and C must 

 be either 6+4 (10) or 6 -4 (2). If, on working out the percentage, it 

 coincides with the theoretical prediction, the method of locating genes 

 in the chromosome receives strong support. In practice, it may 

 be said, the method works out perfectly for short sections of the map, 

 but breaks down somewhat for long map distances, for the reasons 

 indicated below. 



Double crossing-over, an explanation of apparent discrepancies 

 between map distances and crossover percentages. — This matter is 

 best explained by the use of a concrete instance. Let us take three 

 sex-linked genes, white, miniature, and bar. The crossover percent- 

 age observed between white and minature, as has already been shown, 

 is 33; that between miniature and bar is 22. The expected crossover 

 percentage between white and bar is either 33+22 (55) or 33—22 (11), 

 but the observed value is 44 per cent. The proposed explanation of 

 this apparently serious discrepancy is given by the authors of the 

 theory as follows: 



"If we represent the percentages of crossing-over as relative dis- 

 tances along the chromosome the three points will lie as shown in 

 Fig. 84, a. If crossing-over takes place between white and miniature 

 and between miniature and bar, then it might be expected sometimes 

 to take place in both regions at once, as shown in Fig. 84, b. The result 

 here would be to produce two chromosomes like those shown in the 

 lower figure (Fig. 84, c). The combinations of factors which these 

 two chromosomes resulting from double crossing-over would contain, 

 are white long bar and red miniature round. Since these two classes 

 of gametes are actually produced, the results of the experiment fulfil 

 the theoretical expectation. 



